Suppose vector $u = (-2,3)$ and
vector $v = (-5,3)$ then:
$(u + v = ?)$ and
$(u - v = ?)$ and
$(v - u = ?)$ and
$(6u = ?)$ and
$(-1/8v = ?)$ and
$(3u - 4v = ?)$
You add vectors coordinate-wise (coordinate-to-coordinate: the first coordinate of the sum is the sum of the first coordinates of the summands; the second coordinate of the sum is the sum of the second coordinate of the summands, etc). You multiply vectors by scalars coordinate-wise as well (multiply each coordinate by the scalar). You do combinations of vector additions and scalar multiplications by performing the multiplications first and the additions later.
P.S. You are studying for Calculus III and you don't know how to do basic operations with vectors? I confess I find it very hard to believe that this is not contained in your textbook, or was not covered in lecture.
This is the most I'll give - http://en.wikipedia.org/wiki/Vector_(geometric)#Vector_addition_and_subtraction - I feel like this question is too homework-y.